5 papers
Optimal complexity of adaptive FEM for second-order linear elliptic PDEs driven by non-residual estimators, Part I: Symmetric PDEs
Philipp Bringmann, Aleksandar Dadic, Dario Ferloni +3
We consider adaptive finite element methods for symmetric second-order linear elliptic PDEs, where the adaptive algorithm steers the local mesh refinement as well as an iterative a…
Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
Philipp Bringmann, Dirk Praetorius
The Zarantonello fixed-point iteration is an established linearization scheme for quasilinear PDEs with strongly monotone and Lipschitz continuous nonlinearity in Hilbert spaces. T…
Unconditional full linear convergence and quasi-optimal complexity of smoothed adaptive finite element methods
Philipp Bringmann, Christoph Lietz, Dirk Praetorius
We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFE…
Newton's method in adaptive iteratively linearized FEM
Philipp Bringmann, Maximilian Brunner, Dirk Praetorius
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features a…
Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods
Philipp Bringmann
A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to…